Operator Ordering and Classical Soliton Path in Two-Dimensional N = 2 Supersymmetry With Kähler Potential

Abstract

We investigate a two-dimensional N = 2 supersymmetric model which consists of n chiral superfields with Kähler potential. When we define quantum observables, we are always plagued by operator ordering problem. Among various ways to fix the operator order, we rely upon the supersymmetry. We demonstrate that the correct operator order is given by requiring the super-Poincaré algebra by carrying out the canonical Dirac bracket quantization. This is shown to be also true when the supersymmetry algebra has a central extension by the presence of topological soliton. It is also shown that the path of soliton is a straight line in the complex plane of superpotential W and triangular mass inequality holds. One half of supersymmetry is broken by the presence of soliton.

Operator Ordering in Two-Dimensional N = 1 Supersymmetry With Curved Manifold

“…We investigated a operator ordering problem in two-dimensional N = 1 supersymmetric model which consists of n real superfields. In the previous paper [10], we have argued that the supersymmetry gives a basis to fix the operator ordering properly in two-dimensional N = 2 supersymmetry. We can admit that the super-Poincaré algebra gives the correct operator ordering in two-dimensional N = 2 supersymmetry.…”

“…Among several ways for fixing of operator orders, we consider how symmetry decides the proper quantum operator. In the previous paper [10], we have argued that the super-Poincaré algebra gives a basis to fix the operator ordering properly in twodimensional N = 2 supersymmetry. We can admit the supercharge operator Q and Q have a correct operator order when each component fields ϕ satisfy the following relation:…”